Solution for elliptic inclusion in an infinite plate with remote loading and Eshelby’s eigenstrain of polynomial type

In this paper, a particular inhomogeneous inclusion problem is studied. In the problem, Eshelby’s eigenstrain takes the type [Formula: see text], where m+ n = 2, and the remote loadings [Formula: see text], [Formula: see text] are applied. In the solution, the complex variable method is used. The continuity conditions along the interface of the matrix and the inclusion are formulated exactly. Because the stress field is no longer uniform in inclusion in this case, the studied problem has an inherent difficulty. After some manipulation, the final result for stress components [Formula: see text], [Formula: see text] and [Formula: see text] in inclusion are obtainable. In the present study, [Formula: see text], [Formula: see text] and [Formula: see text] are no longer uniform.

Thermal mechanical coupling analysis of two-dimensional decagonal quasicrystals with elastic elliptical inclusion

In this paper, the thermal mechanical coupling problem of an infinite two-dimensional decagonal quasicrystal matrix containing elastic elliptic inclusion is studied under remote uniform loading and linear temperature variation. Combining with the theory of the sectional holomorphic function, conformal transformation, singularity analysis, Cauchy-type integral and Riemann boundary value problem, the analytic relations among the sectional functions are obtained, and the problem is transformed into a basic complex potential function equation. The closed form solutions of the temperature field and thermo-elastic field in the matrix and inclusion are obtained. The solutions demonstrate that the uniform temperature and remote uniform stresses will induce an internal uniform stress field. Numerical examples show the effects of the thermal conductivity coefficient ratio, the heat flow direction angle and the elastic modulus on the interface stresses. The results provide a valuable reference for the design and application of reinforced quasicrystal materials.

Exact solutions of interfacial cracking problem of elliptic inclusion in thermoelectric material

In the present work, the problem for elliptical inclusion with interfacial crack in thermoelectric material is studied. The inclusion and matrix are assumed to be imperfect bonding, which is subjected to uniform heat flux and energy flux at infinity. The interfacial cracking problem of elliptic inclusion in thermoelectric material is investigated by using conformal mapping and complex function method. The complex expressions of temperature field and electric field in inclusion and matrix are obtained. The energy release rate of thermoelectric material under the influence of inclusion is given. The effects of elliptic inclusion with interfacial crack on temperature field and electric potential also are compared by numerical examples. The results show that inclusion reduces the conversion efficiency of thermoelectric material.